You are quite right though - we have radically altered the balance of the system - by 'raising' badgers to the status of 'protected'. Up until then (i.e over the last millenium, before that it was done by wolves, etc.), local keepers would simply maintain their populations at sensible levels. That's why all the above were able to coexist. There has, however, been one other major change that has also made a massive difference to the numbers of badgers produced each year, and that's the widespread farming of cattle maize. Again, I think it unlikely that there have been any studies on this. I can, however, tell you that I spend, on average, about six nights a week out foxing with both NV and thermal imaging, and I see LOTS of badgers. I doubt there are many professional biologists who see as many as I do...